The Effects of Instruction on Children's Understanding of the "Equals" Sign

"equals" sign as "the same as"-that is, as a "relational" symbol (e.g., Behr, Erlwanger, & Nichols 1976, 1980; Van de Walle 1980). Instead, primary school children appear to interpret the sign in terms of action performed, such as "adds up to" or "produces" (Ginsburg 1982). In other words, children appear to view "equals" as an "operator" symbol (a "write something" symbol). As a first grader put it: "It means it would add up to, and whatever the answer was, you'd put it down." It appears that children expect written (horizontal) equations to take a particular form: an arithmetic problem consisting of two (or perhaps more) terms on the left, the result on the right, and in between, a connecting ("equals") symbol (e.g., 3 + 2 = 5). Children tend to reject equations such as 13 = 7 + 6, 6 + 4 = 3 + 7, and-8 = 8, equations that do not adhere to the typical form and easily lend themselves to an operator interpretation of "equals" (see, e.g., Behr et al. 1980; Ginsburg 1982; Nichols 1976). Moreover, Weaver (1971, 1973) found that children had greater difficulty solving for a missing element in an equation when the arithmetic operation (problem) was on the right (e.g., ? = 5 + 8, 13 = 5 + ?, 13 = ? + 8) than when it was on-the left (e.g., 5 + 8 = ?,5 + ? = 13,? + 8= 13). Research typically indicates that viewing "equals" as an operator sign persists through elementary school (e.g., Behr et al. 1976, 1980). Moreover, a restricted understanding of equals may continue into